The generator matrix

 1  0  1  1  1  1 2X^2+X  1  1 2X  1  1  1  0  1  1  X  1 2X^2 2X^2+2X  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2+X  1 2X^2+2X  1  1  0  1  1  1 X^2+2X  X  1 2X  X 2X  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  1  2 2X^2+X 2X^2+X+2  1 2X 2X+2  1 2X^2+2X+1 X+1  0  1 2X 2X+1  1 X+2  1  1 2X^2+X+1  1 2X^2+2 2X^2+X X+2 2X^2+2X+2  0 2X^2+2X+1 2X^2+X X^2+X+2 2X^2 2X+2 2X^2+2X  1  2  1 X^2+X 2X^2  1 2X X+1 X^2+2X+2  1  1 X^2+2X+2  1  1  1 2X^2+2 2X+2 2X+1  0  1 2X^2+X 2X^2+X+1 X^2+1 X^2+2X+2 2X^2+X+1 X+1 2X^2+2X+1  0
 0  0 2X  0 2X^2 2X^2 2X^2  0 2X^2 2X^2 2X^2+2X 2X X^2+2X 2X X^2+2X  X 2X^2+X 2X^2+X 2X^2+X X^2+X  X X^2+X 2X^2+X 2X^2+2X X^2+X 2X^2+X X^2 2X^2 X^2 X^2 2X 2X^2+2X 2X X^2+2X 2X^2+2X  X X^2+X  X  0  0 2X^2+2X  X  X  0 2X^2+X 2X^2  0 2X X^2+X X^2+2X X^2+X 2X X^2+X  0 X^2 X^2 X^2+2X  0 2X^2+X 2X^2+2X 2X^2
 0  0  0 X^2 X^2  0 2X^2 2X^2 2X^2 X^2 2X^2 X^2 2X^2 X^2  0 2X^2 2X^2 X^2 X^2  0  0 X^2 2X^2 X^2  0 X^2 2X^2 X^2  0 X^2  0  0 2X^2  0 2X^2 X^2 X^2 2X^2 2X^2 X^2 2X^2  0 2X^2 X^2 2X^2 2X^2  0  0 X^2  0  0 X^2 2X^2  0 2X^2  0 X^2  0 X^2 X^2  0

generates a code of length 61 over Z3[X]/(X^3) who´s minimum homogenous weight is 114.

Homogenous weight enumerator: w(x)=1x^0+186x^114+252x^115+576x^116+1400x^117+906x^118+1410x^119+2522x^120+1284x^121+1776x^122+3268x^123+1206x^124+1614x^125+1692x^126+630x^127+426x^128+272x^129+18x^130+24x^131+68x^132+54x^133+6x^134+34x^135+12x^136+20x^138+12x^139+12x^141+2x^144

The gray image is a linear code over GF(3) with n=549, k=9 and d=342.
This code was found by Heurico 1.16 in 1.1 seconds.